Step 1 :The problem is asking for the future value of an investment given an initial amount, a rate of return, and a time period. The formula for continuous compounding is: \(A = P * e^{rt}\) where: A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal). t is the time the money is invested for, in years.
Step 2 :In this case, P = $12,000, r = 5.5% = 0.055, and t = 3 years. We can substitute these values into the formula to find A.
Step 3 :Substituting the given values into the formula, we get \(A = 12000 * e^{(0.055*3)}\)
Step 4 :Solving the above expression, we get A = 14152.717424536688
Step 5 :Rounding to two decimal places, the total amount in the account in three years will be \(\boxed{14152.72}\)